ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

2pPA5. Theoretical modeling of nonlinear surface waves.

M. F. Hamilton

Yu. A. Il'inskii

E. A. Zabolotskaya

Dept. of Mech. Eng., Univ. of Texas, Austin, TX 78712-1063

Nonlinear effects in surface waves, like those in bulk elastic waves, are
enhanced dramatically by microinhomogeneous features such as cracks and grains
that are common in rocks. Since surface waves experience less geometrical
spreading loss than bulk waves, nonlinearity can be even more pronounced than in
bulk waves. A brief review of theoretical models for studying nonlinear surface
wave propagation will be presented. The models are based on the theory developed
by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569--2575 (1992)] for nonlinear
Rayleigh waves in isotropic solids. In subsequent articles published in the
Journal the theory was used to study harmonic generation, waveform distortion,
and shock formation in plane waves, cylindrical waves, and diffracting surface
wave beams. Radiation from both time harmonic and pulsed sources was
investigated. Reported values for second- and third-order elastic moduli were
used to calculate coefficients of nonlinearity for a number of rocklike
materials. The theoretical model was recently extended to encompass nonlinear
Stoneley, Scholte, and Lamb waves, and to include effects of anisotropy and
piezoelectricity. Most experiments reported on nonlinear surface waves are
associated with the development of nonlinear SAW devices in the 1970s. Several
of these experiments will be revisited, and new interpretations of the
measurements will be offered. [Work supported by NSF, the Office of Naval
Research, and the Schlumberger Foundation.]